problem solving math board

Math Whiteboard

Math Whiteboard is the First Collaborative Whiteboard designed specifically for Mathematics Teaching and Learning

FREE for teachers, tutors and students

FluidMath Integration

FluidMath is an authoring tool for MathWhiteboard pages. You can save your whiteboards in FluidMath and share copies in MathWhiteboard.com

Learn more about it here > FluidMath Integration

Gallery of Examples

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Click here to see the gallery  > Gallery of examples whiteboards

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Teachers, tutors and students

Start collaborating now! Click the button below and communicate mathematics in the most natural and fluid way with MathWhiteboard.

Embed MathWhiteboard in your site and provide your users with the most fluid collaborative mathematics teaching and learning experience. Click the button below to learn about partnerships.

bring math to life!

Just a few of the great things you can do with math whiteboard, collaborate.

Share the same collaborative math work space with your students

graphing calculator

Mathwhiteboard is like a smart piece of math paper with all of the functionality of a graphing calculator

write or type math

Math entry is easy with handwriting recognition or you can just type your math

Computer algebra system

A full computer algebra system enables calculations from arithmetic to calculus

import pdf files

You can make your pdf assignment files your background

runs in your browser

No installation required, it just runs in your browser on any device, ChromeBook, IPad, Windows Tablet, etc.

And so much more!

MathWhiteboard’s technology is patented: US 9,576,495; US 9,691,294; US 9,773,428; US 10,431,110; US 11,282,410

math whiteboard examples

problem solving math board

systems of equations

Move fluidly between handwritten math, graphs, and solutions

problem solving math board

animate rate of change

Math sketching enables you to connect abstract mathematics notation with concrete examples by making hand-drawn sketches come to life.

problem solving math board

Calculations

From simple arithmetic to Calculus, a powerful Computer Algebra System sits underneath the hood.

problem solving math board

Transformations of Functions

Sliders make it easy to explore functions

problem solving math board

more transformations

Sliders turn abstract concepts into concrete examples

problem solving math board

annotate pdf files

Simply drag and drop pdf files into the whiteboard and then write math and annotations on top

GETTING STARTED WITH MATH WHITEBOARD

InputModes

FluidMath is an authoring tool for MathWhiteboard pages.

You can save your whiteboards in FluidMath and share a copy with MathWhiteboard.com

Whiteboard App

Whiteboard app

Solve problems and explain your thinking in a digital math workspace. 

whiteboard example 1

The Whiteboard app is a digital workspace for teachers and students to solve problems and explain their thinking. Math concepts can be explored in a variety of ways using a flexible set of tools to sketch, write, and build equations.

The Whiteboard app is an open-ended educational tool, ideal for elementary classrooms and other learning environments that use laptops, iPads, or Chromebooks.

App Features

  • Use the Drawing tools to solve problems and show understanding.
  • Add equations, expressions, and descriptions with the Math Text and Writing tools.
  • Hide and reveal work with resizable covers to create your own problems and model strategies.
  • Share your work by saving an image or creating an 8-character code and link to send to others.

Technical Support and Feedback

Please contact our team for app support and feedback.

© 2022 The Math Learning Center

This app was crafted by Clarity Innovations: “We improve teaching and learning by creating solutions that match promising technologies with the needs of education.” www.clarity-innovations.com .

problem solving math board

Before you go, check this out!

There are plenty of other articles to develop your skills and showing you how to make money teaching online!

The 7 Best Online Whiteboards and tools for Teaching Math

When teaching Maths online one of the most useful tools you can have is just like in the physical classroom, a whiteboard.  This article will introduce you to the online whiteboards available and rate them for use with Mathematics.

Which are the seven best online whiteboards for teaching math? There are multiple online software solutions that aid the educational process when it comes to mathematics. However, the seven best online whiteboard apps are:

  • BigBlueButtonBN

GoToMeeting

  Now that you know the ways you can use online whiteboards let’s dig into them a little deeper and compare their features so you can make an informed choice.

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https://scribblar.com

Scribblar is one of the most popular online software solutions that feature an integrated whiteboard. It provides a real-time whiteboard with multiple uses and an advanced yet user-friendly interface. Scribblar is an extremely useful tool for teachers regardless of their subject (mathematics, physics, economics, etc.). It provides useful features, such as

Voice and text chat

  • Multiple users working on the same project

Unlimited space

Privileges that can be restricted, various shapes available.

problem solving math board

Having an integrated voice chat and text function, it allows both the students and the teacher to speak directly using their laptop’s microphone. This is a very important feature when it comes to online teaching.

One of the most important perks of Scribbler is it not limiting its users to attending one-to-one classes. This online whiteboard allows multiple users to take part actively in the class. Not only can the teacher draw and manage the whiteboard but so can the students. The whiteboard supports a wide variety of file formats. One teacher can tutor multiple students at once and conduct group classes as if students were in a physical classroom.

Scribblar includes many useful features for teachers to use. The amount of space that can be used on the online whiteboard is unlimited. There is no need to delete previous work to write something else instead. Next, the teacher can restrict certain users’ privileges when it comes to editing or visualizing the whiteboard content.

This way, you can assign students to work on separate tasks without being able to copy from one another. Because of this feature math teachers can assign equations to each student or group of students. After the students solve the equation the teacher can check the whole method used by the student to solve the problem.

Scribblar also offers a wide variety of shapes that can be drawn on the whiteboard. This means you can materialize complex equations and math problems, without having to upload a PDF to use as a background or as an attachment for students.

You can find the complete subscription plans list at https://scribblar.com/plans .

https://bitpaper.io

This is one of the most popular whiteboards for teaching on the internet right now.  BitPaper has a lot of useful features and an intuitive user interface for both the teacher and the students.

Useful features for teachers:

Online Chat

Audio and video chat, screen sharing, drag and drop.

  • Auto Saving
  • Data import and export

Permanent Web Link (URL)

Supports multiple file formats, limited feature free usage.

problem solving math board

The ability of a student to chat using a shared chat means the students can ask questions while the teacher is presenting their new topic or subject.  It also allows the teacher to share related links to content.

The use of Audio and Video chat means that the nonverbal communication that normally is available in the classroom can come across to the online teaching environment.  The ability to hear the tone and inflection of the student’s voice will let the teacher know if the student really understood.  The use of video chat means the teacher can read the student’s body language for the same reasons.

Screen Sharing

The ability to share your whole screen in a Web Conference style way means that you can show students absolutely anything you can see on your own computer.  You can demo software packages and show students how to complete any task on their own computer with your computer.

Rather than having to click on a button and go searching for a file on your computer using a windows file browser, it is so much simpler to be able to drag and drop directly onto your whiteboard.  It saves time and is more intuitive.

When you are teaching a class, you are juggling heaps of things and even more so in an online class where there is also technology to deal with.  The Autosave feature means the whiteboard is saved periodically so that you do not lose your work and have one less thing to worry about.

Data Import and Export

Mathematics extensively uses data sets for higher math problems and the ability to import and export this data means you don’t have to recreate it in the whiteboard.  It also means you can base your mathematics on real data sets.  Once you have changed that data during the class you can then export the results by downloading them to your computer or to student computers.

This means that the teacher can present, and the students can also be allowed to have access as well in a tutorial style delivery to show understanding.  This increases engagement for the students and helps the teacher clarify topics.

The ability to have a permanent web page link or URL (Universal Resource Locator) means that once the student knows the link they can bookmark.  This means it is easy for them to attend the next class and share with other students.

The ability to support multiple file formats means that you don’t have to convert documents for use with the whiteboard.  Supported file formats are:

  • Images (JPG, BMP, GIF, PNG)
  • Word Documents
  • Adobe PDF Documents

BitPaper is an online whiteboard software solution that can be used for free. However, the free plan limits the use of certain functions. For example, you cannot start calls and you can only submit one paper per month.

Full pricing is available at https://bitpaper.io/pricing/ .

https://ziteboard.com/

Ziteboard online software solution is probably the simplest online whiteboard available on the Internet. It is mainly designed for real-time tutoring. In terms of mathematics teaching, Ziteboard is excellent. It provides a vast amount of unique shapes that are used to make the student understand any content related to math. Its features include:

User-friendly interface

Whiteboard export, great compatibility.

  • Multiple feature free usage plan

The most important feature of this software is the user-friendly interface. Its layout is lightweight and easy to understand, yet powerful, including a lot of advanced visual capabilities.

One unique feature that Ziteboard provides is the availability of the whiteboard as image files. You can export the whole whiteboard as a PNG file or select a certain portion of the screen to export. You can download the whole whiteboard as a high-resolution SVG file compatible with Adobe Illustrator and other vector image editing software. Finally, you can download the entire whiteboard on separate pages as a PDF file.

TIP : Keep in mind that if you want to export the whiteboard as a PDF file, switch on the Display A4 pages feature so that the board’s size will fit A4 size dimensions.

Another aspect that makes Ziteboard a great online whiteboard software solution is compatibility with a lot of different devices. You can install Ziteboard as a:

  • WordPress plugin
  • Google Chrome extension
  • App using Google Play Store

Multiple Feature Free Usage

Regarding its subscription prices, Ziteboard features a Free Starter plan that comprises an unlimited number of public shared whiteboards and real-time collaborators. However, it only provides three whiteboards that can be used before purchasing a Pro plan, and only three basic colors available. The major drawback of the Starter plan includes limited data traffic on the website and on the whiteboards. The most expensive subscription includes an unlimited number of private boards, whiteboards, collaborators, and colors. It also provides unrestricted data traffic on the website and on the whiteboards created.

 To check the full pricing, visit https://ziteboard.com/pricing/ .

BigBlueButton

http://www.bigbluebutton.org

BigBlueButton is an open-source plugin compatible with the Moodle LMS. It provides a lot of distinct features that make the learning process easier and more intuitive, such as

Video, audio, and text chat

Many visual tools.

problem solving math board

This plugin supports real-time sharing of slides and a user-friendly whiteboard integrated within the video call. That this software includes a wide variety of features along with a whiteboard represents an important feature compared to other software solutions available on the Internet.

This is a particularly useful feature when it comes to PowerPoint presentations or tutorials on how to use specific software. However, teaching math does not always fit the screen share feature. The whiteboard feature is more useful because the students can work along with the teacher on solving equations.

The whiteboard offered by BigBlueButton is a multi-user feature, meaning that more than one user can make annotations on the whiteboard and manage the content. You can use screen sharing feature at the same time as the integrated whiteboard, helping you as a teacher, to make important observations related to the shared screen. You can also use the whiteboard as a demonstrational environment where the students can prove the understanding of learned concepts.

Another thing that must be taken into consideration is related to the pricing. Being an open-source plugin, its maintenance is provided by a sizable group of people. This way, there is no need to pay a fee to use the plugin on your Moodle-based website.  As with all open source software be mindful that the support is not guaranteed.  This is something you only get with paid software products.

One important drawback of the BigBlueButton is that its whiteboard does not have a specially designed menu for mathematics. However, the mathematical equations can be solved using an integrated whiteboard in two distinct ways. The first method using a graphic tablet and the built-in pencil tool to draw the equations on the online whiteboard. The second method refers to adding the PDF file containing the equation solution to the workspace so that everyone can understand the solving process.

The whiteboard tool menu comprises different visual tools, such as

  • Pointer thickness
  • Pencil color

Web Conferencing

While these tools are not specifically designed for mathematics, they do however all contain whiteboards with all the common features.  They also have screen sharing to large audiences so can be used in a Lecture style presentation.  The ability to share your screen with many people means you can share your mathematics software packages with large audiences and demo or give tutorials.

Here is a link to an article for 30 free mathematics software packages you could share with your students via a Web Conference.

LINK: Top 30 Best Free Math software you can use

https://www.webex.com

Even though it is not designed for teaching, it provides a lot of helpful features for teachers. Webex supports video conferences as well as screen sharing. Featuring a modern look, its various options include an online whiteboard that can be used for different tasks during the learning process.

Webex feature list includes:

  • Free plan with limited features
  • 25 simultaneous video feeds
  • Video and audio call
  • Multi-monitor support
  • Phone and Tablet Apps

https://zoom.us/

Zoom is one of the most popular video conference online web conference software tools. It is commonly used for business and educational purposes. Its main feature is the generous free plan that can be used after signing up with a valid e-mail address. Another important feature consists of the option to blur or change your background during the video call. This is especially useful during classes.

To put it in a nutshell, there are many amazing features available on Zoom:

  • Free plan with a generous amount of features
  • Background Blur
  • Up to 100 people per call

Note: Using the free plan, a call can only last up to 40 minutes.

https://www.gotomeeting.com/

This web conference software hosts video conferences. GoToMeeting is commonly used for business meetings. However it has multiple uses when it comes to e-learning as it features an integrated whiteboard. This feature helps teachers tutor multiple students by explaining using a customizable workspace.

GoToMeeting includes many features, such as:

  • Mobile apps for Android and iOS
  • Up to 100 people in the conference
  • Advanced encryption of the meeting

PRO TIP – Safety Online

To protect yourself and not let people know your real IP address you can use Virtual Private Network Software in conjunction with your webconference software. This is more important when you are doing public web conferences where you may not know who is attending. The one I use is IP Vanish and it also has the added benefit of me being able to watch more TV Shows and Movies from multiple countries on platforms like Netflix.

Next Must Read Articles

ARTICLE: Are Online Math Classes Easier or Harder? (It Depends) ARTICLE: 15 Practical Tips for Teaching your First Online Class

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problem solving math board

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Explore Math. Together.

I love, love how students are able to see and hear each other . It's an ideal tool for creating online engagement with students.

Math Jam lets us talk, share the marker, and build off one another's work, just like we were sharing a whiteboard in the classroom .

I like that both my students and I can upload, drag, and drop images and PDFs directly onto the canvas!

I love that I can put a problem on each of the students' individual whiteboards.

I love that Math Jam has video, audio, and chat built in.

Ready to Jam?

Why math jam.

  • Grades 6-12
  • School Leaders

Live Event: Cool Ways to Teach with Graphic Novels!

20 Math Bulletin Board Ideas That Make Learning Fun

Math has never looked better!

Math bulletin board feature image

Looking for fresh ideas to motivate your math students? Why not give one of these creative math bulletin board ideas a try? You’ll find interactive options like the Math Boggle game board, as well as classics with a twist like the #MathTalk word wall. Whether you’re teaching simple addition or more complex computations, there’s a bulletin board here for you!

Our Favorite Math Bulletin Boards

1. how to learn math.

problem solving math board

Math isn’t so scary with this flow chart! Show your students how simple learning about math can be.

Source: Pinterest: Robin Humberstad

2. Do You Want To Build a Polygon?

Bulletin board with words Do you want to build a polygon?

Teaching about geometry? We love this interactive puzzle board for learning about polygons.

Source: All Aboard the Patti Wagon 

3. Math Detectives

Bulletin board with words Be a math detective!

Create a bunch of math riddles for this detective math bulletin board. Your students will feel like Sherlock Holmes!

Source: Frogs and Cupcakes

4. Gumball Math

board with words Havin' a ball with... addition and subtraction- math bulletin board ideas

How cute is this math gumball machine? Students will love making equations with this interactive math bulletin board.

Source: Pinterest: Martha Guiza

5. Even and Odd Street

Bulletin board with words Even and Odd street

Make teaching about even and odd numbers fun. Students can draw the houses for this bulletin board idea.

Source: Pinterest: Leah Downey

6. Boggle Math

Bulletin board with words Boggle math

Once they learn how to play, your class will be asking you to play Math Boggle all the time.

Source: The Routty Math Teacher

7. We Are Mathematicians

Bulletin board with words We are mathematicians- math bulletin board ideas

Inspire your class to use math skills in their future careers. The possibilities are endless!

Source: Rise Over Run

8. Tryangles

Bulletin board with words the best angle from which to approach a problem is the TRYangle

If at first you don’t succeed, try(angle) again! These smiling shapes will brighten up your classroom.

Source: Pinterest: Sandy Kadar

9. It Makes Cents

Bulletin board with words It makes cents

Teach all about money with this interactive grocery store bulletin board. Students can “shop” at the store. What fun!

Source: Pinterest: Elizabeth Dubberly 

10. Valentine Fractions

Board with words we love fractions and hearts- math bulletin board ideas

Looking for an educational Valentine’s board? Fractions have never been more fun!

Source: 4 the Love of Teaching 

11. Looking at Problem-Solving

Bulletin board with words Lets look at problem solving

Take a look at this problem-solving bulletin board—those googly eyes are beyond cute.

Source: Instagram: Classroom Inspirations

12. Handy Calculator Help

Bulletin board with words Scientific Graphic Calculators

Calculators can be tricky to understand. This bulletin board idea is a handy reference for students still learning to use them.

Source: Math Equals Love

13. Gee-I’m-a-Tree

Bulletin board with colorful leaves and words Gee-Im-A-Tree- math bulletin board ideas

This geometry bulletin board idea is un-be-leaf-able!

Source: Pinterest: Amy Alferman

14. Math Talk

Bulletin board with words Math Talk

We love this math bulletin board idea! Your students will be #MathTalk experts in no time.

Source: Pinterest: Marissa Doll

15. Stuck on Math Problems

Bulletin board with words Stuck on a problem?

When your students are stuck on a problem, they can refer to this handy board. There are so many ways to problem-solve!

Source: Pinterest: Caroline | Boldly Inspired Curriculum | High School Math

16. Know Your Math Facts

Bulletin board with words Know your facts!- math bulletin board ideas

Showcase math facts with this fun, colorful board.

Source: Pinterest: Lotts of Learning

17. Math Is Everywhere

Bulletin board with words Math is Everywhere!

This board shows your students how important math is in everyday life. Math is all around us!

Source: Twitter: ONTS Special Needs

18. We’re Lovin’ Math

Bulletin board with words Math We're lovin in!

Fries make math fun! Use empty fast-food french fry containers to make this interactive math bulletin board.

Source: Pinterest: Brittany Gerber

19. Factor Flowers

Board with words Factor flowers and flowers in pots- math bulletin board ideas

Have your class make their own factor flowers to display on this bulletin board. Flower power!

Source: Apples and ABC’s

20. Candy Corn Addition

Bulletin board with candy corn

This board is perfect for Halloween, or you can switch out the candy shape to fit any season.

Source: Facebook: Bulletin Board Ideas for Elementary School Teachers 

Did you enjoy these math bulletin board ideas? Check out our science bulletin board ideas too!

Plus, for more articles like this, be sure to subscribe to our newsletters .

Math has never looked better than when using one of these 20 creative math bulletin board ideas for the classroom!

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Using Interactive Whiteboards with Mathematics Teachers and Students

David Glassmeyer and Melissa Paurowski

Kennesaw State University 

In this blog post, we (1) describe the technological tool of interactive whiteboards, (2) summarize how interactive whiteboards can be used to teach mathematics in ways aligned with research, (3) overview the top free interactive whiteboard platforms available in Sept. 2021, and (4) explain how we have used digital whiteboards in our work with mathematics teachers and students.

1. What are interactive whiteboards?

Interactive whiteboards are digital environments with multimodal features (text, images, symbols, drawings) that provide a shared space between teacher and learners that is both accessible and directly manipulative (De Vita et al., 2018). Students can collaboratively edit a digital whiteboard to share ideas, solve problems, or reach a consensus in small groups. Interactive whiteboards can usually be saved and exported for continued work, sharing, and archiving. Figure 1 shows an example of how we used an interactive whiteboard with high school students solving the staggered pipe problem , and Figure 2 displays the teacher overview page to see our entire class of students’ work.

Figure 1: Example of collaborative work being completed on the interactive whiteboards platform Whiteboard.fi , with the teacher feedback options shown at the bottom.

problem solving math board

Figure 2: The teacher view from Whiteboard.fi , displaying a class of students’ work.

problem solving math board

2. What does research say about using whiteboards for teaching mathematics?

From research on traditional/physical interactive whiteboards (e.g. Smartboards), we know these tools can be used to support students’ academic achievement, positive attitudes, classroom management, knowledge construction, learner engagement and interactivity, motivation, and visual quality (Balta & Duran, 2015; Higgins, 2010; Holmes, 2009; İpek & Sözcü, 2016; Warwick et al. 2011). We also know traditional/physical interactive whiteboards can reinforce traditional, teacher-centered pedagogical styles, as often only teachers control the board and students begin focusing only on visual appeal rather than the content itself (Holmes, 2009; Smith et al., 2005, 2006; Torff & Tirotta, 2010). Just like other technological tools, the key in whiteboard effectiveness is about how teachers use the tool.

As for digital interactive whiteboards (e.g. Whiteboard.fi ), there are similar themes, though less research is available (Erdener & Kandemir, 2019). When used with active and collaborative pedagogical approaches, interactive digital whiteboards can help students to improve their cognitive learning across all currently available interdisciplinary research reports (Shi, et al., 2021). Like other technological tools, frequency of use impacts students’ perceived efficiency and perceived learning (Fuchs, 2021). Effective patterns for using interactive whiteboards in mathematics occur in ways supporting research-based practices, for example supporting problem-solving and for organizing mathematical work, reflections, and representations (De Vita et al., 2018; Kutluca et al., 2019; Kohen, 2019; Shi et al., 2018, 2021).

Incorporating interactive whiteboards in classroom instruction can align with research-based practices overviewed in the Mathematics Teaching Principles (NCTM, 2014). Teachers can provide students opportunities to engage in productive struggle as they collaboratively tackle mathematical ideas and problem solve on the whiteboards (De Vita et al., 2018). Teachers can elicit and use evidence of student thinking by saving, sharing, and reviewing student work completed on the whiteboard during instructional time or completed outside of class. The use of whiteboards can facilitate mathematical discourse by allowing students the opportunity to share and build upon ideas together by analyzing and comparing mathematical work in real time (Ball et al., 2018).

3. What is the best interactive whiteboard platform for teaching mathematics?

Several interactive whiteboard platforms currently exist. Table 1 overviews the pros and cons of several currently available digital whiteboards. Our evaluation was conducted in September 2021; given the rapid change of these technologies, the information might become outdated as features, pricing models, and websites come and go. Note we evaluated only the free version of each whiteboard platform and ranked our listing from the best to worst for working with mathematics teachers, and for mathematics teachers using the platform within professional learning contexts or using the platform to teach students mathematics. We also ran the list by 20 in-service mathematics teachers, who supported the ranking.

Table 1: Our top 5 interactive whiteboard platforms, ranked based on their free version’s ability to facilitate mathematics instruction.

Here are other interactive whiteboards we evaluated but did not make our top list:

  • https://miro.com/online-whiteboard
  • https://myviewboard.com/
  • https://whiteboardfox.com/

4. How might you use interactive whiteboards within mathematics teacher education?

With students : As education is evolving, teachers continually seek to improve instructional strategies to reach all students. Learning to reach students both virtually and in-person has challenged us to pursue engaging ways to connect with our students. It is critical that teachers employ methods to formatively assess our students, and interactive whiteboards give us the opportunity to collaboratively work with students throughout a lesson to gain an understanding of their comprehension. These whiteboards allow us to individually reach out to students during a lesson to answer questions or make corrections to student work in real time. This can be particularly beneficial when teaching students virtually. We can see the students’ thought process as they work and help guide students back on track if they become puzzled while working or are unsure how to proceed on a particular problem. It brings the virtual student into a more “in-person” environment to get the one-on-one support from their teacher, while also engaging the students in the classroom. We encourage teachers to consider the many ways virtual whiteboards might be incorporated to allow students to collaboratively problem solve, such as solving equations, labeling geometric figures, notating mathematical proofs, working alongside helpful images and figures, and interacting with virtual manipulatives.

Within PLCs : Students are not the only ones who can benefit from these interactive whiteboards – they are excellent for collaboration among teachers working in Professional Learning Communities (PLCs) and consistency teams. Teachers meeting face-to-face or virtually can utilize the interactive whiteboards to review student work as a team, plan and execute upcoming lessons, review and analyze formative assessment data, and much more. Most of the whiteboard programs allow you to save and share work, which means teachers can continue their collaboration at each PLC meeting. Whether teachers are presenting professional development to their colleagues or leading a grade-level instructional planning meeting, interactive whiteboards can improve collaboration and encourage creative work spaces for us to improve our instruction as we strive to reach all students in our classrooms. 

Within professional development and coursework : Whether the coursework is for undergraduate pre-service teachers attaining initial certification, or in-service teachers attaining graduate degrees, interactive whiteboards have the ability to foster virtual collaboration on mathematical tasks and problems. We have used interactive whiteboards to facilitate problem solving within small groups during synchronous course meetings. In large or small group professional development sessions, interactive whiteboards are a strong tool to link teachers’ ideas together as they work collaboratively. Teachers have the ability to work, plan, and edit during the PD session, then save and continue their work when they get back to their PLC, all via the interactive whiteboard. Whiteboards can also be helpful in connecting instructors with learners during online coursework or professional development, as it gives the instructor the ability to watch as the learners work together and share ideas. Instructors can then adjust and/or pivot the training, real-time, to meet their learners where they are in the learning process.  

Ball, L., Drijvers, P., Ladel, S., Siller, H. S., Tabach, M., & Vale, C. (2018).  Uses of technology in primary and secondary mathematics education . Cham, Switzerland: Springer.

Balta, N., & Duran, M. (2015). Attitudes of students and teachers towards the use of interactive whiteboards in elementary and secondary school classrooms. TOJET: The Turkish Online Journal of Educational Technology, 14 (2), 15-23.

De Vita, M., Verschaffel, L., & Elen, J. (2018). The power of interactive whiteboards for secondary mathematics teaching: Two case studies.  Journal of Educational Technology Systems ,  47 (1), 50–78.

Erdener, K., & Kandemir, M. A. (2019). Investigation of the reasons for students’ attitudes towards the interactive whiteboard use in mathematics classrooms.  International Journal of Research in Education and Science ,  5 (1), 331–345.

Fuchs, K. (2021). Preparing students for success in a changing world: The role of virtual whiteboards in the modern classroom.  Education Quarterly Reviews ,  4 (1).

Higgins, S. (2010) The impact of interactive whiteboards on classroom interaction and learning in primary schools in the UK. In M. Thomas & E. C. Schmid (Eds.), Interactive Whiteboards for Education: Theory, Research and Practice (pp. 86-101). Hershey, PA: IGI Global.

Holmes, K. (2009). Planning to teach with digital tools: Introducing the interactive whiteboard to pre-service secondary mathematics teachers. Australasian Journal of Educational Technology, 25 (3), 351-365.

İpek, İ., & Sözcü, Ö. F. (2016). Preferences and attitudes for using interactive whiteboards in different courses and learning. European Journal of Contemporary Education, 15 (1), 173-184.

Kohen, Z. (2019). Informed integration of IWB technology, incorporated with exposure to varied mathematics problem-solving skills: its effect on students’ real-time emotions.  International Journal of Mathematical Education in Science and Technology ,  50 (8), 1128-1151.

Kutluca, T., Yalman, M., & Tum, A. (2019). Use of interactive whiteboard in teaching mathematics for sustainability and its effect on the role of teacher.  Discourse and Communication for Sustainable Education ,  10 (1), 113-132.

National Council of Teachers of Mathematics (2014). Principles to actions: Ensuring mathematical success for all . Reston, VA: NCTM.

Shi, Y., Peng, C., Yang, H. H., & MacLeod, J. (2018). Examining interactive whiteboard-based instruction on the academic self-efficacy, academic press and achievement of college students.  Open Learning: The Journal of Open, Distance and e-Learning ,  33 (2), 115-130.

Shi, Y., Zhang, J., Yang, H., & Yang, H. H. (2021). Effects of interactive whiteboard-based instruction on students’ cognitive learning outcomes: A meta-analysis.  Interactive Learning Environments ,  29 (2), 283-300.

Smith, H. J., Higgins, S., Wall, K. & Miller, J. (2005). Interactive whiteboards: Boon or bandwagon? A critical review of the literature. Journal of Computer Assisted Learning, 21 , 91- 101.

Smith, F., Hardman, F. & Higgins, S. (2006). The impact of interactive whiteboards on teacher-pupil interaction in the National Literacy and Numeracy Strategies. British Educational Research Journal, 32 (3), 443-457.

Torff, B., & Tirotta, R. (2010). Interactive whiteboards produce small gains in elementary students’ self-reported motivation in mathematics.  Computers & Education ,  54 (2), 379-383.

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problem solving math board

42 Amazing Math Bulletin Board Ideas For Your Classroom

by Sara Ipatenco

Math is one of the core subjects taught at all grade levels. It’s also one of those subjects where students need visuals to help them learn and retain information. That’s where math bulletin boards come in! Create a few visually appealing math-themed boards to remind your students of math concepts in a fun, eye-pleasing, memory-making way.

Here are over 42 fun math bulletin boards!

1. list problem-solving strategies.

Problem solving math bulletin board

Students learn numerous strategies for problem-solving. Create a bulletin board reminding students of all these strategies. When homework or test time comes around, students can simply glance at the bulletin board to remind them to draw a picture, to figure out a subtraction problem, or make a list to find the answer to a word problem.

2. Make it scientific

Math periodic table

A periodic table to elements doesn’t have to stay in the science classroom! Create a table of math elements to remind students what each part of a problem is. Not only is this visually appealing, but it will help students remember important math vocabulary, including types of angles and shapes, decimals, and the different terms in geometry.

3. Teach math language

Problem solving terms_42 Amazing Math Bulletin Board Ideas For Your Classroom

There are many terms associated with addition, subtraction, multiplication, and division that students need to know and remember when reading math problems from their textbook. A table of math language on a bulletin board can be just the thing to help get these terms into their brains. Separate the board into four sections and hang up those key terms. When students see them on a math problem, the board will help them remember what method they need to use to solve the problem.

4. Make a word wall

Word wall_42 Amazing Math Bulletin Board Ideas For Your Classroom

Word walls are typically used to teach spelling and vocabulary words, but they can be useful in teaching math terms as well. If your math class is learning about fractions, hang up decorations related to those key math terms. Add some visual aids and your students will find learning a new and tricky concept much easier and more fun.

5. Show that math is useful

Math is useful_42 Amazing Math Bulletin Board Ideas For Your Classroom

Teachers have all heard the old, “What will I ever use this for?” lamentation in response to hard math. Create a bulletin board showing how useful math is in all areas of life. Choose several professions or activities and write a short description of how math is used. You’ll see the lightbulbs going off as students realize just how important math really is.

6. Tell a number story

Number story_42 Amazing Math Bulletin Board Ideas For Your Classroom

Make a kid-centered bulletin board by having students create their own number stories. This can be a great get-to-know-you activity at the beginning a new math class. It also gives students a visual way to introduce themselves with numbers.

7. Use a math-themed alphabet

Vocab wall_42 Amazing Math Bulletin Board Ideas For Your Classroom

All primary school teachers have an alphabet posted somewhere in their classroom. Why not use a math-themed alphabet? Students will still have access to an alphabet, but they will also learn the definitions of 26 math concepts.

8. Go on a treasure hunt

Math treasure hunt

Create a math-themed treasure hunt, such as adding and subtracting fractions or adding and subtracting money. As students solve problems, they will get closer to the treasure, which could be a fun math activity as a class or a little extra recess.

9. Do an art project

Make math fun with art!_42 Amazing Math Bulletin Board Ideas For Your Classroom

Teach math concepts with a fun art project in place of book work. Robots, for example, can be used to teach how to find the area of a shape in an entertaining and visual way. It’s more fun and more likely that kids will remember the lesson. These math bulletin boards are so fun and visually appealing!

10. Set some math goals

Matholutions

Ring in the new year or start a new school year by having your students make some math resolutions. Perhaps they want to memorize all the multiplication facts or become better at fractions. Create a fun party-themed bulletin board celebrating all these future accomplishments.

11. Tell some jokes

Math jokes_42 Amazing Math Bulletin Board Ideas For Your Classroom

Kids love jokes, and they love to laugh, so incorporate some math jokes into a bulletin board for some added classroom fun. Even better – use math jokes that also teach or reinforce a math concept you’ve already taught.

12. Use candy

Math-themed candies_42 Amazing Math Bulletin Board Ideas For Your Classroom

Replace the actual name of a package of candy with a math pun leading students to the answer. Hang up the new and math improved candy wrappers on a bulletin board. Students will have a ton of fun trying to figure out what kind of candy each one is.

13. Make a math word game

42 Amazing Math Bulletin Board Ideas For Your Classroom

Create a game that encourages students to find key math terms hidden in a puzzle of letters. Take the lesson even further by having students write the definitions or show an example of each word they find.

14. Show place value

Place value chart_42 Amazing Math Bulletin Board Ideas For Your Classroom

Place value is one of those math concepts that is tricky to remember because students must go backwards instead of forward as they might when solving other math equations. A bulletin board that colorfully illustrates place value is a great way to help students learn and remember this tricky math concept.

15. Make wanted posters

Wanted poster bulletin board_42 Amazing Math Bulletin Board Ideas For Your Classroom

This is a great bulletin board for teaching geometrical concepts. Students choose a shape and then create a wanted poster describing that shape. The posters will become a learning guide for the other students. Kids are much more likely to recall the characteristics of each shape this way versus simply reading the definitions from a math book.

16. Track student progress

Math progress board_42 Amazing Math Bulletin Board Ideas For Your Classroom

Set up a bulletin board that keeps track of student progress as they memorize their addition, subtraction, multiplication, or division facts. Once all the students have mastered their facts, the class can celebrate with an ice cream party. Talk about fun!

17. Display art arrays

Math arrays

Arrays can be a visually stunning way to teach students how to multiply. Instead of simply having students draw circles or squares, however, turn the task into an art project. Create arrays that look like windows on high rise buildings and create math bulletin boards of downtown scenes. Or use donut shapes and have students make arrays filling boxes with donuts. In addition to being fun, these visual images will stick with students as they do their multiplication homework.

18. Make mistakes

problem solving math board

The old saying tells us that mistakes are proof we are trying, but students rarely enjoy making those mistakes. Instead, you make the mistakes! Hang up several math problems on a bulletin board and see if students can find the mistakes. Once students find the them, encourage them to solve the problem correctly.

19. Use pictures

problem solving math board

Teach hard math concepts, such as the Pythagorean theorem, using pictures. Even older students enjoy the chance to draw and color, and this can be combined with solving the actual problem as well. Once complete, the pictures can hang on a bulletin board to help teach other students how to solve similar problems.

20. Make it a challenge

Math challenge

Set up a math challenge on a bulletin board. Students will complete a series of tasks to solve the problem. As they solve, they can color or get clues to solve one last tricky math equation. Students will love to do math with this engaging bulletin board!

21. Show an example

Concept breakdown example

Remind students of the method for solving a new concept, such as long division, with a large example on a bulletin board. Break the problem down into steps and use key terms to help students remember how to solve equations.

22. Practice telling time

Teach telling time

Post several clocks on a bulletin board that tell students what time different subjects and activities begin. This is a great way for students to practice recognizing time, and it can also prevent those “how long until…” questions!

23. Celebrate great work

Featured great work on

Instead of a refrigerator to display excellent work, create “The Fridge” on a bulletin board. Allow students to hang math assignments or tests they are especially proud of on the board. Even better – you choose a few great examples and praise those students for their hard work.

24. Teach math talk

Math talk sentence starters

Teach students how to talk themselves through hard math problems by putting questions they can ask on display. Often, thinking about different ways to figure out an answer is all it takes to encourage students to keep working until they are successful.

25. Give them the answer

Backward word problems-42 Amazing Math Bulletin Board Ideas For Your Classroom

Create a bulletin board showcasing your students’ word problem solving skills. Give each students a blank word problem drawing and writing page with an answer written on it. Students will then create a word problem that gets them to the answer provided.

26. Make a giant timeline

Timeline

Reinforce the concept of telling time by having students make clocks on paper plates to create a timeline of the day. Each paper plate will show a time that the class does something, such as go to recess or have math class. Students can also illustrate what the students are doing at each time.

27. Hang some memes

Math meme bulletin board_42 Amazing Math Bulletin Board Ideas For Your Classroom

Kids love memes! There are so many math memes out there, and you can use them to create fun math bulletin boards. Invite students to find and bring in memes to add to the board.

28. Make reference rings

Reference rings

Put together some little reference cards showing students the steps in a certain type of problem or defining key math terms. When students get stuck on a problem, they can grab a reference ring to help them figure it out.

29. Have kids make it

Student made board_42 Amazing Math Bulletin Board Ideas For Your Classroom

Who says you have to make all the bulletin boards? Give students a subject, such as patterns, and have them create a board. Research suggests that when kids teach a concept, they are much more likely to remember it. It’s a win-win – you save time creating the board, and the students remember what you’ve taught them!

30. Play Sudoku

Math sudoku

This number strategy game is a great way to build in some extra math practice. Hang a large sudoku grid on a bulletin board and allow students to make a move when they have a few minutes of free time.

31. Show that math can be magic

Math magic_42 Amazing Math Bulletin Board Ideas For Your Classroom

Hang up some math concepts that seem quite magical! In addition to being eye-catching, students will also learn a lot about math concepts that only look tricky. Once they understand the magic, the problems will be a lot easier to solve.

32. Use cute pictures

Cute geometric shapes

A cute bulletin board is sure to catch the attention of your students. Using fun graphics will entice students to look at the board, and, while they are looking, they will also be learning!

33. Make it hands-on

Math manipulatives_42 Amazing Math Bulletin Board Ideas For Your Classroom

Reinforce addition with a hands-on math problem. Perhaps you’ll use marshmallows in hot cocoa or conversation hearts in February. Give students an addition problem and have them solve it using the hands-on manipulatives. Then they can glue them onto a picture, and you’ll have an easy and fun bulletin board.

34. Uncover hidden math

Hidden math

There are so many math rules that can trick up your students. Reveal those hidden concepts with math bulletin boards. The students will be able to use the bulletin board as a resource during math class, which will boost their overall understanding of those tricky math concepts.

35. Find math in nature

Natural math board

Take a few pictures of math in nature, such as a number made from leaves or rocks or a geometrical shape in the clouds. Invite students to find math in nature, take a picture, and bring it in to add to your nature math bulletin board.

36. Make shape monsters

Math monsters

Showing flashcards is one way to teach 2D shapes, but a fun art project is a more effective way to ensure your students remember the lesson. Have students create shape monsters using several different shapes. Students should describe their monsters to the rest of the class using the names of the shapes they created. Hang the monsters on a bulletin board to help students remember what they’ve learned.

37. Remind students to check their work

Check your answers

Much of math is going back and checking work to make sure students have reached the correct answer. Use something relevant to students, such as a selfie, to help them remember the steps to checking their work properly. Chances are this bulletin board will result in more careful work from your students!

38. Put it on the floor

Math hopscotch

Don’t limit yourself to bulletin boards on the wall. Instead, create a practice hopscotch board on the floor for students to work on math concepts. They can hop fractions from 0 to 1 or hop as they skip count by 2s, 5s, or 10s. Whatever they are practicing will be more fun and engaging because they get to jump while they do it.

39. Give them a true or false mission

True or false math mission

Provide students with a number and several math problems. Their job is to figure out which math problems result in the number you’ve given them, and which ones don’t. Display their work on the board to show the many ways their number can be reached.

40. Keep track of data

Data wall

Keeping track of your students’ data doesn’t have to be boring. It doesn’t have to be kept in a notebook either! Instead, post the grids and graphs on a bulletin board and have students color in their sections as they reach their math goals and objectives. You’ll be able to quickly see your students’ progress and your classroom will look extra beautiful at the same time!

41. Give a math-themed reminder

Inspiring math boards

Teach students other things, such as kindness, using math-themed bulletin boards. A giant calculator can be the starting point for any number of reminders, such as “Calculate Kindness.”

42. Show off what students can do

Bulletin board math accents

Give your students eye-pleasing, fun templates and have them solve problems right on them. Once the kids color them or add accents, you’ll have ready-made bulletin board pieces that both look good and show how awesome and smart your students are!

Math bulletin boards make any classroom more fun and enjoyable. You can make math come alive with these ideas – or use them to spark new ideas to make math more fun for your students!

What’s on your teacher wish list? Let’s discuss in the  #teacherlife community .

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Math Coach's Corner

What IS Problem-Solving?

Ask teachers about problem-solving strategies, and you’re opening a can of worms! Opinions about the “best” way to teach problem-solving are all over the board. And teachers will usually argue for their process quite passionately.

When I first started teaching math over 25 years ago, it was very common to teach “keywords” to help students determine the operation to use when solving a word problem. For example, if you see the word “total” in the problem, you always add. Rather than help students become better problem solvers, the use of keywords actually resulted in students who don’t even feel the need to read and understand the problem–just look for the keywords, pick out the numbers, and do the operation indicated by the keyword.

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 use and recommend.

Another common strategy for teaching problem-solving is the use of acrostics that students can easily remember to perform the “steps” in problem-solving. CUBES is an example. Just as with keywords, however, students often follow the steps with little understanding. As an example, a common step is to underline or highlight the question. But if you ask students why they are underlining or highlighting the question, they often can’t tell you. The question is , in fact, super important, but they’ve not been told why. They’ve been told to underline the question, so they do.

The problem with both keywords and the rote-step strategies is that both methods try to turn something that is inherently messy into an algorithm! It’s way past time that we leave both methods behind.

First, we need to broaden the definition of problem-solving. Somewhere along the line, problem-solving became synonymous with “word problems.” In reality, it’s so much more. Every one of us solves dozens or hundreds of problems every single day, and most of us haven’t solved a word problem in years. Problem-solving is often described as  figuring out what to do when you don’t  know what to do.  My power went out unexpectedly this morning, and I have work to do. That’s a problem that I had to solve. I had to think about what the problem was, what my options were, and formulate a plan to solve the problem. No keywords. No acrostics. I’m using my phone as a hotspot and hoping my laptop battery doesn’t run out. Problem solved. For now.

If you want to get back to what problem-solving really is, you should consult the work of George Polya. His book, How to Solve It , which was first published in 1945, outlined four principles for problem-solving. The four principles are: understand the problem, devise a plan, carry out the plan, and look back. This document from UC Berkeley’s Mathematics department is a great 4-page overview of Polya’s process. You can probably see that the keyword and rote-steps strategies were likely based on Polya’s method, but it really got out of hand. We need to help students think , not just follow steps.

I created both primary and intermediate posters based on Polya’s principles. Grab your copies for free here !

problem solving math board

I would LOVE to hear your comments about problem-solving!

problem solving math board

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Do you tutor teachers?

I do professional development for district and schools, and I have online courses.

You make a great point when you mentioned that teaching students to look for “keywords” is not teaching students to become better problem solvers. I was once guilty of using the CUBES strategy, but have since learned to provide students with opportunity to grapple with solving a problem and not providing them with specified steps to follow.

I think we’ve ALL been there! We learn and we do better. 🙂

Love this article and believe that we can do so much better as math teachers than just teaching key words! Do you have an editable version of this document? We are wanting to use something similar for our school, but would like to tweak it just a bit. Thank you!

I’m sorry, but because of the clip art and fonts I use, I am not able to provide an editable version.

Hi Donna! I am working on my dissertation that focuses on problem-solving. May I use your intermediate poster as a figure, giving credit to you in my citation with your permission, for my section on Polya’s Traditional Problem-Solving Steps? You laid out the process so succinctly with examples that my research could greatly benefit from this image. Thank you in advance!

Absolutely! Good luck with your dissertation!

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1.3: Problem Solving Strategies

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  • Michelle Manes
  • University of Hawaii

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

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

How to Solve It

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

George_Pólya_ca_1973.jpg

George Pólya, circa 1973

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

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

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

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

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

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

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

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

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

Problem Solving Strategy 2 (Try Something!).

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

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

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

Think/Pair/Share

After you have worked on the problem on your own for a while, talk through your ideas with a partner (even if you have not solved it). What did you try? What did you figure out about the problem? This problem lends itself to two particular strategies. Did you try either of these as you worked on the problem? If not, read about the strategy and then try it out before watching the solution.

Problem Solving Strategy 3 (Draw a Picture).

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

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

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

Problem Solving Strategy 4 (Make Up Numbers).

Part of what makes this problem difficult is that it is about money, but there are no numbers given. That means the numbers must not be important. So just make them up!

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

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

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

(Squares on a Chess Board)

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

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

Think / Pair / Share

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

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

Problem Solving Strategy 5 (Try a Simpler Problem).

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

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

Problem Solving Strategy 6 (Work Systematically).

If you are working on simpler problems, it is useful to keep track of what you have figured out and what changes as the problem gets more complicated.

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

Problem Solving Strategy 7 (Use Manipulatives to Help You Investigate).

Sometimes even drawing a picture may not be enough to help you investigate a problem. Having actual materials that you move around can sometimes help a lot!

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

Problem Solving Strategy 8 (Look for and Explain Patterns).

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

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

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

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

(Broken Clock)

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

index-12_1-300x282-1.png

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

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

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

Problem Solving Strategy 9 (Find the Math, Remove the Context).

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

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

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

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

Problem Solving Strategy 10 (Check Your Assumptions).

When solving problems, it is easy to limit your thinking by adding extra assumptions that are not in the problem. Be sure you ask yourself: Am I constraining my thinking too much?

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

index-13_1-300x296.png

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

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Teaching with Jennifer Findley

Upper Elementary Teaching Blog

Math Bulletin Boards for Upper Elementary

Pinterest is full of well-designed and authentic bulletin boards for literacy, but very few for math. In fact, when I am planning my classroom, my mind goes straight to literacy instead of math. Once I realized I was doing that, I actively worked to change and add in more relevant and meaningful math bulletin boards in my classroom.

This post shares SIX low prep, but super meaningful math bulletin boards that you can use in your classroom. Hint: The students are doing the majority of the work on these!

Want to have more math themed resources in your room? Check out this post for math bulletin boards that work great for upper elementary,

Math Word Wall

Math word walls can be very powerful instructional tools. Here is why:

1.) They keep math concepts and terms fresh and “in the mind” of students all year.

2.) They are fabulous resources for students to use when writing in math class.

2.) They can be great transition fillers to review.

Want to make it even more meaningful? Have the students create the words for the word wall. If you have a large unit with lots of vocabulary words, divide them up among pairs or small groups. If you just have a few, assign specific words to your class and then let them select (or you) the ones that are the most helpful to go on the word wall.

Have your students create the words for your word wall to make it more meaningful. Read more math bulletin board ideas on this post.

Problem Solving Bulletin Board

Another bulletin board idea that I love is having a problem solving board titled “We Are Problem Solvers” or something similar. On this board (or wall space), you could display problem solving strategies that you teach AND examples of student work that used that strategy. Not only will this board serve as a reminder of what you have taught but the examples will also serve as mentors for the students.

Click here to read about the specific problem solving strategy that I teach and that my students “love.”

Writing About Math Bulletin Board

I have noticed a huge shift over the year with a push for more writing across the curriculum. To meet this need, you could have a writing about math bulletin board or wall space that shares strategies for writing (sentence stems and mentor examples). And of course, you could also display great examples of writing in math by your students. You could title the board “We Write in Math” and add to it throughout the year.

You could use the following for mentor examples:

  • current student examples
  • past student examples (I like to save really good examples and use them year after year)
  • released examples from the state
  • teacher created models

Here are some example sentence stems:

  • First I … Next I…. Finally I….
  • I added/subtracted/multiplied/divided because the problem said….
  • To begin with, I…
  • I know my answer is correct because….

Need some help getting your students writing in math? Check out this blog post for several ideas to support your students’ writing in math class.

“We Use Math Vocabulary” Board

Another option is to have a math vocabulary board with examples of student work that use math vocabulary.  This is similar idea to the above board but with a heavy focus on students using academic vocabulary . I love this math bulletin board idea because my students often struggle putting in academic vocabulary in their explanations. Having a focus on it would show the importance and celebrate when students use academic vocabulary in their work. This could be near your math word wall or even an extension of it.

Show What You Know Board

I also dedicate one of my bulletin boards (or sometimes wall space, depending on my classroom) to the math concept we just learned. I keep it very simple (for me), but also quite rigorous for the students.  The students create posters to show what they know about a math skill or concept.

I use printables from this my 5th Grade Math Bulletin Board Printables , which includes a printable for every 5th grade math standard. I love using these because the students have to show what they know in a variety of ways, one of which usually requires explaining in writing. Also, I let the students decorate them when they are finished. They love decorating them and it makes them pop when we hang them up.

Want to have more math themed resources in your room? Check out this post for math bulletin boards that work great for upper elementary,

If you would like to see these 5th Grade Math Bulletin Board Posters in my TeachersPayTeachers store, click here.

Math in Real Life Bulletin Board

A final option, and one of my favorites is to create a “math is real life” board were students bring in or sketch examples of math they see in real life titled “We Use Math in Real Life.” Or another option is to title it “Math is Everywhere” as shown in this example from Middle School Math Man (click on the picture to head over to his blog post to read more about this board idea).

Want to have more math themed resources in your room? Check out this post for math bulletin boards that work great for upper elementary,

Photo Credit: Middle School Math Man

There you have it! My favorite math bulletin board ideas for math. Click here to grab headers for each bulletin board idea shown.

Want to have more math themed resources in your room? Check out this post for math bulletin boards that work great for upper elementary,

Do you use any of these math bulletin boards or any others not listed here? Share in the comments!

Share the Knowledge!

Reader interactions.

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July 14, 2017 at 12:03 am

Love these ideas! Everything is very cross-curricular and it’s great to see math in hand with writing.

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July 30, 2017 at 12:42 pm

I would a copy of your student friendly mathematical practices. I just can’t friend them.

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August 15, 2017 at 6:47 pm

Jennifer, I love your ideas. Do you have a template for the vocabulary word wall? I think it is an awesome idea to have the students create the vocabulary word for the word wall. My email is [email protected] . Thank you soooo much!

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August 19, 2017 at 11:39 pm

Hi Kat, you can grab it here (it is the second to last page): https://drive.google.com/file/d/0B8DtIUhMGc9qTVN4UlltZ21tLVk/view

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December 22, 2017 at 2:05 pm

the abope subject is very important as say prof dr mircea orasanu and prof horia orasanu

January 7, 2018 at 2:10 pm

sure the above can applied in more cases as say prof dr mircea orasanu and prof horia orasanu as followings MECHANICS OF CONSTRAINTS AND NON HOLONOMY Author Horia Orasanu ABSTRACT In this subsection, we define a constraint function for the head angle of the robot. In particular, we use a line-of-sight (LOS) guidance law as the reference angle for the head link. LOS guidance is a much-used method in marine control systems (see, e.g. [27]). In general, guidance-based control strategies are based on defining a reference heading angle for the vehicle through a guidance law and designing a controller to track this angle [27]. Motivated by marine control literature, in [17] based on a simplified model of the snake robot, using cascade systems theory, it was proved that if the heading angle of the snake robot was controlled to the LOS angle, then also the position of the CM of the robot would converge to the desired path. We will show that a similar guidance-based control strategy can successfully steer the robot towards the desired path. However, we perform the model-based control design based on a more accurate model of the snake robot which does not contain the simplifying assumptions of [17] which are valid for small joint angles

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February 18, 2019 at 11:11 pm

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March 3, 2019 at 7:25 am

and in bulletin board must to consider

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April 7, 2019 at 1:46 pm

and it is known the resources that ,then so

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Welcome Friends!

I’m Jennifer Findley: a teacher, mother, and avid reader. I believe that with the right resources, mindset, and strategies, all students can achieve at high levels and learn to love learning. My goal is to provide resources and strategies to inspire you and help make this belief a reality for your students.

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Teaching Through Problem-solving

An elementary-age male student points while his female teacher stands beside him and observes

  • TTP in Action
The key to effective boardwork is doing the problem yourself and then anticipating how your students will solve it. It is from this perspective you monitor, select, and sequence the student work to share on the board. —Alex Johansen-Laughlin Prieto Math and Science Academy, Chicago

Board Organization

  • Revisit each element of the lesson as needed–the problem, a key model or illustration, classmates’ solution strategies, etc.
  • See the “story” of the lesson, from the initial problem, through the solutions and insights developed by the class, to the summary of what they learned
  • Compare different solution strategies and consider how their own thinking relates
  • See the mathematical expression, visual model and verbal description associated with each solution strategy
  • Experience an organized model for their own note-taking and reflection
  • Become “meta-cognitive” as they see how new ideas are developed in mathematics

A teacher diagrams a student's mathematical idea as it is being explained by a student

Sample Board

Notice the features of the sample board below, and imagine how consistent organization of the board in this way might benefit your students.

  • The problem posed to students is shown at the upper left of the board, so students can refer back to it.
  • The “learning goal” captures the problem as we hope students will pose it themselves.
  • The “ friend’s idea” section of the blackboard captures student thinking and the student solution methods you select for presentation, in the order you want to discuss them, along with key information such as visual and mathematical models.
  • The “summary” includes the mathematical points you hope to draw out of neriage (“kneading”) discussion.

problem solving math board

Japanese board writing often seems spontaneous, since it features ideas and student work that emerge during the lesson. In fact, teachers typically plan board writing in advance, as they think about the key ideas and models on the board that will spark, capture and advance students’ thinking.

International comparisons reveal that Japanese mathematics teachers use the board more frequently than do teachers in Germany and the U.S., and that Japanese teachers tend to keep the board writing throughout the lesson, rather than erasing parts of it during the lesson. The board writing provides a record of the lesson that students can consult as they summarize and reflect on what they learned.

Teachers often find that creating a board plan provides an opportunity to think through the whole lesson–from posing the problem, to choosing and sequencing student work that will be shared, to identifying the key ideas that will emerge from the neriage discussion and the summary.

Smartboard users can consider how to use their chosen technology to provide similar supports for students to actively build the new mathematical ideas. Video clips from Akihiko Takahashi’s lesson  Ways of Counting and Mathematical Expression  and Joshua Lerner’s lesson  Conceptual Understanding of Multiplication  provide some ideas for smartboard users.

Blank Board Plan Templates

problem solving math board

Blank Board Plan Template (PDF)

problem solving math board

Can’t find a resource you need? Get in touch.

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50 Delightfully Inventive Math Bulletin Board Ideas

  • Topics : Classroom Ideas Inspiring Teachers

Thavius Nelson - TeacherVision Contributor

Transform your math classroom into a vibrant and inspiring learning environment with '50 Math Bulletin Board Ideas.' From geometry to algebra, this article has everything you need to create engaging visual displays for your students.

math bulletin board ideas

Math is an essential part of our everyday lives. Getting high school and middle school students excited about math class is necessary. As a math teacher, you’ve considered things to do for your classroom decor of exciting tidbits to make numbers, symbols, and subtraction come alive for your students. TeacherVision can help you jazz up your classroom bulletin boards with polygons, number lines, and decimals.

What are some good math bulletin board ideas?

1. be a problem solver.

2. Math Talk

3. Math Collage

4. Growth Mindset

5. Math Tree

6. Every Problem Has a Solution

7. Mathematicians

8. Math Word Walls

9. How To Rock At Math

10. Math is All About

11. #MathTalk 2

12. Math Joke of the Week

14. Everything Math

16. Figure Me Out

17. Think You Don’t Need Math?

18. Why Math?

19. Take a Bite Out of Word Problems

20. Everyone Has Value

Math art project resource for board worthy content:  Tessellations Worksheets

21. Math to Make You Laugh

22. Have You Used Math Today?

23. Math Helps Us Bloom

24. We Are Mathematicians, Also Known As

25. So Many Reasons To Love Math

26. Place Value

27. Math Pennants

28. Algebra II Bulletin Board

29. Operation Equation

30. The Slope of a Line

31. Current Algebra Topics

32. Our New Year Matholution

33. How To Learn Math

34. Matchbook Bulletin Board

35. C.U.B.E.S.

Math art project resource for board worthy content:  Art Activity Choice Board for Elementary

36. We Know The Magic In Math

37. #MathTalk 3

38. Math Teaches Us How To

39. Math Is Sweet

40. Math Is All About

41. Math the Med

42. Gee-I’m-A-Tree!

43. Math Funhouse

44. Math Selfie

45. Fraction Sundaes

46. Having a Ball with Addition and Subtraction

47. Word Problems Crack the Code

48. Decoding Division

49. Formula

50. It’s Pizza Time

What do you put on a math bulletin board?

Teachers become amazing creators out of necessity to successfully teach students essential concepts that will affect their lives. Maybe your spring bulletin board for middle school math class needs updating or your high school math class requires a boost. Many teachers put up math posters, play games , teach vocabulary, and implement problem-solving strategies to encourage classroom engagement.

Every year is different. Your back-to-school bulletin board ideas help set the tone for the year. After a few months, some teachers change their rooms to reflect their student's pulse. Having, "I can" statements on the walls or using Halloween as a foundation to incorporate math concepts helps to appeal to a young mind.

How do you make an interesting bulletin board?

Many teachers have found having interactive bulletins or whiteboards can help with learning and classroom management. Tying the lesson to current events is always suitable for many ideas for making exciting bulletin boards. If you get stuck on ideas, TeacherVision has many math teaching resources to help create a dynamic classroom.

If you teach 8th-grade math, you can help prepare students for the adjustment to high school.

What is a good math problem to put on a bulletin board?

It’s not a math classroom without a stimulating math problem in plain sight. Of course, your bulletin board display will depend on what kind of math you are teaching. The primary math sequence in Georgia (Algebra, Geometry, Algebra II, Precal) fosters classroom ideas such as aligning it to something within everyday life.

Students think they are clever when asking, " When will I ever use this?” The students have yet to learn what their life would be without math. As a teacher, you can easily open their eyes to what is needed to help them succeed. Surprise your students by putting a practical math problem on your classroom door. Give them extra points for solving it and explaining why it's an important life skill.

Math affects every part of our lives, and students must have a solid understanding of it. What visuals do you have in your math classroom to help students learn?

Looking for more math support?

Head over to our Maths Subject Resource Hub where you'll find a trove of resources for printable templates, worksheets, cutouts, math classroom decorations, lesson plans, handprints, and writing prompts to simplify your teaching during the school year.

Sign up for the TeacherVision newsletter to get daily or weekly updates on everything new and coming up in the world of teaching. Create a free TeacherVision account to start downloading your free teaching resources and lesson plans from our huge library of resources and too.

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Thavius Nelson - TeacherVision Contributor

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Math = Love

Problem Solving Strategies Posters and Bulletin Board

By: Author Sarah Carter

Posted on Published: August 10, 2012  - Last updated: March 16, 2023

Categories Math Posters , Math Bulletin Boards

This blog post contains Amazon affiliate links. As an Amazon Associate, I earn a small commission from qualifying purchases.

Want to check out my favorite Amazon items for the classroom? Check out my Amazon favorites page !  

Less than a week until school starts.  I still have so much to do.  I did complete one of my bulletin boards today. This is my new Problem Solving Strategies Posters and Bulletin Board.

problem solving strategies posters and bulletin board - high school math classroom decorations

I got to use my new toy: a Laminator !  The school has a giant laminator in the teacher’s lounge, but you have to get the person with the key to help you use it.  And, every time I’ve tried to get the person with the key to help me use it, they haven’t been at school. 

So, I ordered my own small laminator .  It’ll be perfect for when I have an epiphany at ten pm and decide that I need something laminated for my lesson the next day.   

MATH = LOVE RECOMMENDS…

drawing of laminator machine with text

A laminator is a MUST-HAVE for me as a math teacher! I spent my first six years as a teacher at a school with a broken laminator , so I had to find a way to laminate things myself.

I’ve had several laminators over the years. I currently use a Scotch laminator at home and a Swingline laminator at school.

  • Scotch Laminator
  • Swingline Laminator
  • Nuova Laminating Pouches

I highly recommend splurging a bit on the actual laminator and buying the cheapest laminating pouches you can find!

I’m seriously addicted to laminating .  I pretty much want to laminate everything in my house right now.  I’d show you all the other cool stuff I laminated , but it’ll have to wait until I can actually put it up in my classroom. 

I laminated my door decorations , but I can’t put them up until they finish staining my door…

But, I did get to finish my Problem Solving Strategies Bulletin Board today.  And, yes, I hate the pipes and cable running in front of my bulletin board as much as you do.  This is what happens when you teach in a school that was built in 1919.  I have random pipes all over my room. 

I love the building, but it definitely comes with its challenges.  The original slate chalk boards are still on the wall.  They’ve just been covered up.  And, I’ve got a radiator along one wall.  Does it still work?  I have no clue.  I guess I’ll figure that out come winter time…  So much to learn!    

If you want to create your own, I uploaded the problem solving strategies posters I made as a PDF file.  I just printed them on Astrobrights paper (another new favorite!)  

I’ve also hung these posters on the wall below my Smart Board before.

problem solving strategies posters

You might also be interested in a page of problem solving strategies I created for students to glue in their interactive notebooks.

Free Download of Problem Solving Strategies Posters

Problem Solving Strategies Posters (PDF) (2208 downloads )

Want more posters to decorate your classroom? Check out my posters page !

More Free Printable Math Posters

divisibility rules printable chart pdf.

Mrs. Hinson

Saturday 10th of June 2017

Ms. Hagan You are amazing! Thank you so much for your posts and sharing your resources. As a new teacher I appreciate it!

Saturday 26th of September 2015

Just found these...Thanks for sharing!!

Sarah Carter (@mathequalslove)

Monday 5th of October 2015

You're welcome! I posted an updated set a few weeks ago if you're interested!

Wednesday 21st of August 2013

these are so awesome!! thank you!

Wednesday 28th of August 2013

You're welcome!

Friday 16th of August 2013

Since reading your blog, I've gotten the laminator out of the closet and have gone wild laminating everything I can (even begging the baseball coach next door to me if I can laminate stuff for him).

I completely understand. :) I just ordered 300 more laminating sheets. I think I'm addicted...

Saturday 11th of August 2012

Thanks for including the PDF of the posters!! I'm going to use a couple in my room :)

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Intervention based on science of reading, math boosts comprehension, word problem-solving

Students working on math problems at a chalkboard.

Mon, 04/29/2024

Mike Krings

LAWRENCE — New research from the University of Kansas has found an intervention based on the science of reading and math effectively helped English learners boost their comprehension, visualize and synthesize information, and make connections that significantly improved their math performance.

The intervention, performed for 30 minutes twice a week for 10 weeks with 66 third-grade English language learners who displayed math learning difficulties, improved students’ performance when compared to students who received general instruction. That indicates emphasizing cognitive concepts involved in the science of reading and math are key to helping students improve, according to researchers.

“Word problem-solving is influenced by both the science of reading and the science of math. Key components include number sense, decoding, language comprehension and working memory. Utilizing direct and explicit teaching methods enhances understanding and enables students to effectively connect these skills to solve math problems. This integrated approach ensures that students are equipped with necessary tools to navigate both the linguistic and numerical demands of word problems,” said Michael Orosco, professor of educational psychology at KU and lead author of the study. 

The intervention incorporates comprehension strategy instruction in both reading and math, focusing and decoding, phonological awareness, vocabulary development, inferential thinking, contextualized learning and numeracy.

“It is proving to be one of the most effective evidence-based practices available for this growing population,” Orosco said.

The study, co-written with Deborah Reed of the University of Tennessee, was published in the journal Learning Disabilities Research and Practice.

For the research, trained tutors developed the intervention, developed by Orosco and colleagues based on cognitive and culturally responsive research conducted over a span of 20 years. One example of an intervention session tested in the study included a script in which a tutor examined a word problem that explained a person made a quesadilla for his friend Mario, giving him one-fourth of it, then needed to students to determine how much remained.

The tutor first asked students if they remembered a class session in which they made quesadillas, what shape they were and demonstrated concepts by drawing a circle on the board, dividing it into four equal pieces, having students repeat terms like numerator and denominator, and explaining that when a question asks how much is left, subtraction is required. The students also collaborated with peers to practice using important vocabulary in sentences. The approach both helps students learn and understand mathematical concepts while being culturally responsive.

"Word problems are complex because they require translating words into mathematical equations, and this involves integrating the science of reading and math through language concepts and differentiated instruction," Orosco said. "We have not extensively tested these approaches with this group of children. However, we are establishing an evidence-based framework that aids them in developing background knowledge and connecting it to their cultural contexts."

Orosco , director of KU’s Center for Culturally Responsive Educational Neuroscience, emphasized the critical role of language in word problems, highlighting the importance of using culturally familiar terms. For instance, substituting "pastry" for "quesadilla" could significantly affect comprehension for students from diverse backgrounds. Failure to grasp the initial scenario can impede subsequent problem-solving efforts.

The study proved effective in improving students’ problem-solving abilities, despite covariates including an individual’s basic calculation skills, fluid intelligence and reading comprehension scores. That finding is key as, while ideally all students would begin on equal footing and there were little variations in a classroom, in reality, covariates exist and are commonplace.

The study had trained tutors deliver the intervention, and its effectiveness should be further tested with working teachers, the authors wrote. Orosco said professional development to help teachers gain the skills is necessary, and it is vital for teacher preparation programs to train future teachers with such skills as well. And helping students at the elementary level is necessary to help ensure success in future higher-level math classes such as algebra.

The research builds on Orosco and colleagues’ work in understanding and improving math instruction for English learners . Future work will continue to examine the role of cognitive functions such as working memory and brain science , as well as potential integration of artificial intelligence in teaching math.

“Comprehension strategy instruction helps students make connections, ask questions, visualize, synthesize and monitor their thinking about word problems,” Orosco and Reed wrote. “Finally, applying comprehension strategy instruction supports ELs in integrating their reading, language and math cognition… Focusing on relevant language in word problems and providing collaborative support significantly improved students’ solution accuracy.”

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Math Craft Activities Growing Bundle | Bulletin Board Ideas | Problem-Solving

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Description

Introducing the ultimate solution for making math fun and exciting! Your students will love showing off their math skills with these fun craft activities. You will love having a simple, academic bulletin board for each season!

This exclusive growing bundle of math crafts is designed to provide a hands-on learning experience for young minds to acquire and master key math concepts with ease.

Currently Included

  • September: Apple Fact Families (addition & subtraction)
  • October: Skip Counting Spiders (by 2s, 3s, 5s, 10s, and 25s)
  • November: Problem-Solving Pies (addition, subtraction, multiplication, and division word problems)
  • December (1): Word Problem Wreaths (addition, subtraction, multiplication, and division)
  • December (2): Subtraction Stockings (2- & 3-digit subtraction with and without regrouping)
  • January: Snowman Math Craft (addition, subtraction, multiplication, and division)
  • February: Valen-TIME Heart Craft (time to the nearest hour, half-hour and quarter-hour)
  • April/May: Measurement Garden Craft (measuring objects to the nearest 1/4 inch and 1/2 centimeter

This is the LOWEST price the bundle will be.

The Complete Bundle will include

  • a minimum of 15 math crafts
  • PLUS bulletin board accessories/headings

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problem solving math board

New Orleans teens solve 2,000-year-old math problem

W hen she started a math contest with a bonus question challenging students to create a new proof for the Pythagorean theorem using trigonometry, teacher Michelle Blouin Williams didn’t expect anyone to complete the task.

“I was just looking for some ingenuity,” she said, per CBS News .

Calcea Johnson and Ne’Kiya Jackson, however, blew Williams’ expectations out of the water by figuring it out in 2023. The teens were seniors at St. Mary’s Academy in New Orleans, a prestigious Catholic school for girls which has maintained a 100% acceptance rate to colleges and 100% graduation rate for 17 years, CBS News reported.

They appeared in an episode of CBS News’ “60 Minutes ” on Sunday to talk about their achievement.

How did the teens find the answer?

While they were motivated initially by the math competition’s $500 prize, an internal drive to finish what they started manifested when they reached the tricky bonus question. For two months, the high school seniors worked tirelessly to finish their proof.

CeCe Johnson, Calcea’s mother, told “60 Minutes,” “It was pages and pages and pages of, like, over 20 or 30 pages for this one problem.”

Her father, Cal Johnson, added, “Yeah, the garbage can was full of papers, which she would, you know, work out the problems and — if that didn’t work she would ball it up, throw it in the trash.”

When they finished, teachers at St. Mary’s recognized the importance of their work and submitted their proof to the American Mathematical Society for recognition at a conference in March 2023, where the students presented their work.

What is the Pythagorean theorem and what’s a proof?

In essence, the mathematical theorem states that knowing the lengths of two sides of a right triangle enables you to figure out the length of the third using this formula: a² + b² = c².

It’s associated with Greek mathematician Pythagoras, but evidence suggests it was known earlier, in Babylon and Iron Age India, per Britannica . Its practical uses include construction and architecture, two-dimensional navigation, and surveying.

A mathematical proof is exactly what it sounds like: reasoning that proves a mathematical theorem is true. American mathematician Daniel Kane explains proofs as being like essays, but using math.

Why is Calcea Johnson and Ne’Kiya Jackson’s work significant?

According to the “ 60 Minutes ” episode, “there had been more than 300 documented proofs of the Pythagorean Theorem using algebra and geometry, but for 2,000 years a proof using trigonometry was thought to be impossible.”

In 1927, mathematician Elisha Loomis said as much in his book, “ The Pythagorean Proposition .” Loomis argued that there could be no trigonometric proof of the theorem because it would be circular.

Stuart Anderson, a professor emeritus of mathematics at Texas A&M University–Commerce, told Scientific American , “A lot of the basic trig ‘identities’ are nothing more than Pythagoras’ theorem.”

So, because trigonometric functions are based upon the Pythagorean theorem, using them reflexively to prove the theorem would be akin to going in circles and a fundamental mathematical error, Loomis argued.

According to Scientific American , the teens refuted this in their presentation in 2023 and said that “a trigonometric identity called the law of sines didn’t depend on the Pythagorean theorem and that they could use it to prove the theorem.”

Calcea and Ne’Kiya have joined an extremely small group who’ve accomplished the same feat, including mathematician Jason Zimba, who successfully created a new proof in 2009. The two submitted their proof for final peer review this spring and continue to work on creating more proofs.

How did the world respond to their accomplishment?

The teens were given the keys to the city of New Orleans and a commendation from the governor of Louisiana, among other public recognitions.

While their achievement “blew up,” as Ne’Kiya described it, the two students remain humble, and laughed at being called geniuses.

When news of their accomplishment broke, some people seemed to be shocked and dismissed the news as fake, St. Mary’s president Pamela Rogers said in the interview .

“They were saying, ‘Oh, they could not have done it. African Americans don’t have the brains to do it.’ ... People — have a vision of who can be successful. And — to some people, it is not always an African American female. And to us, it’s always an African American female.”

When interviewer Bill Whitaker asked why they thought there’d been such a response, Ne’Kiya said, “Probably because we’re African American, one. And we’re also women. So I think — oh, and our age. Of course our ages probably played a big part.”

“I’d like to actually be celebrated for what it is. Like, it’s a great mathematical achievement,” she continued.

Calcea Johnson and Ne-Kiya Jackson sat for an interview with CBS News 60 minutes, which aired on Sunday May 5, 2024, to discuss their achievement. The two teens created one of the first trigonometric proofs of the Pythagorean Theorem.

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